Appendix VI.
diagram A M B. The line A B is w say, or 56 Ibs. per sq. ft. ;
then the dotted radii, r^ r^ r3 &cv will shew the value of n for the
respective divisions. The total force on each area being repre-
sented by an arrow, its magnitude will be n h'b', or 56 x ^1 x h' bf.
These values are next set out in the vector figure below on lines
parallel to the forces taken in order, as o i, i 2, 2 3, 3 4, &c., and
o 9 will be the magnitude of the resultant which passes through
the intersection of the first and last link in the link polygon, and
also through the centre A of the roof.
Moments in Link Polygons. — Four forces in Fig. 963 are
treated in the usual manner, and a vector figure obtained where
the pole O has been placed at a known perpendicular distance A
963.
rom the resultant o 4, Nothing but distances should be measured
on the space diagram, and forces only on the vector figure. In
the former the resultant is placed at Q, where the first and last
links intersect. Let it now be required to find the moment of the
resultant round the point p, and draw line p ef parallel to the
direction of the resultant. Naturally the moment will be o 4 x q.
But it is also O N x ef where */is the intercept between the first
and last links. For proof, 004 and Q/<? are similar triangles :
hence —
and